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| Home > Publications database > Nahordnung und Wechselwirkungen in der Legierung Ni$_{0.89}$Cr$_{0.11}$ |
| Home > Publications database > Nahordnung und Wechselwirkungen in der Legierung Ni$_{0.89}$Cr$_{0.11}$ |
| Book/Report | FZJ-2018-02537 |
1985
Kernforschungsanlage Jülich, Verlag
Jülich
Please use a persistent id in citations: http://hdl.handle.net/2128/18228
Report No.: Juel-2004
Abstract: The aim of this work has been to measure the short-range order of the alloy Ni$_{0.89}$Cr$_{0.11}$ in a state of thermal equilibrium in order to obtain informationabout the atomic interaction energies. The existence of the coherently ordered phases that should appear at lower temperatures are derived from these interaction energies. The method of diffuse neutron scattering has been used to determine the short-range order. A new spectrometer with a multidetector and energy-analysis(separation of the inelastic background) was built, where most of the measurements were performed. The sample was a single crystal. Monoistopic $^{58}$Ni was used in order to improve the relation between signal and incoherent background. The short-range order produces a broad peak at the scattering vector (1$\frac{1}{2}$ O). It's intensity is about 1.6 times higher than the Laue scattering of a totally disordered alloy. In spite of the low degree of short-range order and lattice distortions 35 short-range order parameters and 15 distortion parameters have been determined. The short-range order parameters have a typical accuracy of 0.1 % for different atomic distances. The observed distortions of the lattice are very small, less than 1/1000 of the lattice parameter. From the measured short-range order absolute values of the effective pair interactions have been calculated in two different ways. The new Invers Monte Carlo Method (Kern), which is free of approximations, leads to nearly identical results as those found by the commonly used high-temperature approximation (Krivoglaz, Clapp, Moss). This demonstrates for the first time that reliable results can be expected from the high-temperature approximation in its region of applicability if statistical errors are taken into accountby a weighted linear least squares analysis. The pair interactions between Ni and Cr are of long range and oscillating. which indicates that their origin is dued to conduction electrons. The spatial dependence of the pair interaction can be well described by an anisotopic Friedel-potential. The fermi surface of NiCr$_{0.11}$ is also imaged in the diffuse scattering pattern and is similar to the known fermi surface of ferromagnetic nickel. Since the Inverse Monte Carlo Method makes it possible to include many-body interactions, for the first time reliable statements on many-body interactions in an alloy can be made from experimental data. Only three-body interactions are found to exist between nearest neighbors, in agreement with predictions from theoretical calculations (Bieber and Gautier). The existence of four-body interactions could not be proved. With the knowledge of the interactions the equilibrium states of the fcc NiCr alloy can be determined as a function of temperature and concentration by means of statistical thermodynamics. For this purpose the Monte Carlo Method has been used. The amount of CPU-time required for this has been decreased by a new parallel alogrithm. For the first time a larger number of experimental determined interactions have been included in the calculation of the coherent phase diagram. The results reproduce the known Ni$_{2}$Cr phase and predict an additional ordered structure Ni$_{3}$Cr (DO$_{22}$). The small difference between the calculated and observed values of the transition temperature of Ni$_{2}$Cr must have a physical meaning. Factors that could contribute to this disagreement are changes in the interaction energies caused by lattice contraction accompaning the ordering process, the dependence of interactions on concentration, or the role of the disregarded long range part of the pair-interaction.
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